ANSWERS, ETC., TO EXERCISES GIVEN. 401 
not exhibit nerve-signs, or with the girls in general. As the association 
amongst those who do not exhibit nerve-signs is quite as high ss for the girls 
in general, the ‘‘ conclusion ” quoted does not seem valid. 
2. (1) 2) (1) (2) 
per per per per 
thousand. thousand. thousand. thousand. 
(B)/N 3:2 75 (4)/N) 0-9 4-0 
(4B)/(4) 149 117 | (4B)/(B) 40 63 
(BOC) 38°8 62-0 (40)/(C) 6°6 18-8 
(4BO)[(4C) 216 214 (4BO)[(BC) 36°8 638 
The above give the two simplest comparisons, either of which is sufficient to 
show that there is a high association between blindness and mental derange- 
ment amongst the deaf-mutes as well as in the general population ; amongst 
the old, the association is, in fact, small for the general population, but well- 
marked for deaf-mutes. This result stands in direct contrast with that of 
Qu. 1, where the association between the two defects 4 and D was much 
smaller in the defective universe 8 than in the universe at large. As previously 
stated, no great reliance can be placed on the census data as to these infirmities. 
3. If the cancer death-rates for farmers over 45 and under 45 respectively 
were the same as for the population at large, the rate for all farmers 15— 
would be 1°11. This is slightly less than the actual rate 1:20, but the excess 
would not justify the statement that ‘‘ farmers were peculiarly liable to cancer.” 
It is, in point of fact, due to the further differences of age-distribution that we 
have neglected, e.g. amongst those over 45 there are more over 55 amongst 
farmers than amongst the general population, and so on. 
4. 15 per cent. 
6. If 4 and B were independent in both C and 4 universes, we would have 
(4 B) equal to . - 
471x419 151x139 
617 T 383 =374"7. 
Actually (4B) only=358. Therefore 4 and B must be disassociated in one or 
both partial universes. 
9. (1) 68°1 per cent. (2) 42'5 per cent. The fallacy discussed in § 2 is 
now avoided, and there seems no reason for declining to consider this as evidence 
of the effect of expenditure on election results. 
10. The limits to y are— 
y<i(Bz-22-1) 
> H(z +2a?), 
subject to the conditions yz, y<{0, y<22-1. No inference of a positive 
association from two negatives is possible unless z lies between the limits 
"382... 618 ie 
11. The limits to ¥ are :— 
(1) y<3(6x- 622-1) 
> (x + 622), 
subject to conditions y<0, {4x -1, pe. 
An inference is only possible from positive associations of 4 Band 4C if =p 
t ; an inference is only possible from two negative associationsif lies between 
211 . . . .and 274. . . . Note that = cannot exceed 3. 
(2) y<¥(6x—3x*-1) 
> 4(22 + 322), 
subject to conditions y<40, (52-1, p=. 
26